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Note that the angle imparted on the object ball relative to the direction of momentum of the cue ball is the angle between a line drawn from the centre of the cue ball through the centre of the object ball at the moment of contact, and a line drawn from the centre of the cue ball in the direction of its momentum before contact occurs. The angle is trivially calculated by noting that the hypotenuse of the black triangle in the diagram is 2 radii of either ball (assuming equal sized balls), and the length of the side opposite to the angle in question is 1 radius, thus the angle is given by the inverse sine of ½, which is 30°.

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